Introduction to Statistics

transcript

INTRODUCTION TO STATISTICS

Statistics

Singular sense(Cowden & Oxden) A statistical tool Used for collection, presentation, analysis &

interpretation of numerical data

Statistics

Plural sense(Proff. Horace Secrist) Aggregate of facts Affected by multiplicity of causes Numerically expressed Collected for predetermined purpose Comparable

Importance and Scope of Statistics

Statistics in Planning Statistics in State Statistics in Mathematics Statistics in Economics

Statistics in Business and Management Statistics in Accountancy and Auditing Statistics in Industry Statistics in Insurance Statistics in Astronomy

Statistics in Physical Sciences Statistics in Social Sciences Statistics in Biological and Medical Sciences Statistics in Psychology and Education Statistics in War

Measures of Central Tendency

Arithmetic Mean Geometric Mean Harmonic Mean Median Mode

Arithmetic Mean

Sum of set of observations divided by number of observations

Arithmetic Mean

DiscreteSingle Continuous

Geometric Mean

Set of n observations in nth root

Harmonic Mean

Reciprocal of arithmetic mean

Median

Value of the variable which divides the group into two equal parts

Median

Continuous

Single/Discrete Exact Median

Value which has greatest frequency density

Measures of Dispersion

Range Quartile Deviation Mean Deviation Standard Deviation

Difference between two extreme observations

Range = Xmax - Xmin

Merits of Range

Easiest to compute Rigidly defined Requires very less calculation

Demerits of Range Not based on entire data Affected by fluctuations of sampling Cannot be used with open end

classes Not suitable for mathematical

treatment

Quartile Deviation

Measure of dispersion based on upper quartile and lower quartile

Merits of Quartile Deviation

Makes use of 50% of data, which is better than range

Can be used with open end classes

Demerits of Quartile Deviation

Affected by fluctuation of sample Not suitable for further

mathematical treatment

Mean Deviation

Arithmetic mean of the absolute deviations

Merits of Mean Deviation

Based on all observations Less affected by extreme

observations than S.D. Better measure of comparison

Demerits of Mean Deviation

Ignores sign of deviation Rarely used in sociological studies Cannot be used with open end

classes

Standard Deviation

Positive square root of the arithmetic mean of the squares of the deviations from their mean

Considered as most important and widely used measure of dispersion

Merits of Standard Deviation Rigidly defined Based on all observations Suitable for further mathematical

treatment Least affected by fluctuations of

sampling

Demerits of Standard Deviation

More affected by extreme items Relatively difficult to calculate and

understand

Correlation

A statistical measure Used to study degree of

relationship between two or more variables

Types of CorrelationCorrelation

Simple

Positive & Negative

Linear & Non-linear

Partial

Multiple

Simple Correlation

Study under only two variables. Example,Height & Weight of personFamily income & ExpenditurePrice & demand

Positive and Negative Correlation

Positive if both variables moves in same direction. Example,Day temp. & Sales of ice-creamHeight & Weight

Positive and Negative Correlation

Negative if variables move in opposite direction. Example,Price & DemandDay temp. & Sales of sweater

Linear & Non-linear Correlation

Linear if unit change in one variable bring constant change in other variable. Example,

X 1 2 3 4 5

Y 5 10 15 20 25

Linear & Non-linear Correlation

Non-linear if unit change in one variable doesn’t bring constant change in other variable. Example,

X 1 2 3 4 5

Y 4 10 12 13 20

Partial Correlation Study under two variables at a time

keeping other variables constant. Example,Relationship between production and seed quality keeping fertilizer constant

Multiple Correlation Study relationship between one

variable & combined effect of other variables. Example,Relationship between production and combined effect of seed quality & fertilizer

Methods of Studying Correlation

Scatter diagram method Karl Pearson’s method Rank correlation method Bivariate frequency method

Scatter diagram method Graphical and simplest method of

finding correlation between two variables

One variable is plotted on the horizontal axis and the other is plotted on the vertical axis

Interpretation of data

Perfect positive correlation

Perfect negative correlation

High degree of positive correlation

High degree of negative correlation

Low degree of positive correlation

Low degree of negative correlation

No correlation

Karl pearson’s method

Mathematical method for studying relationship between variables

Two methods of calculatingDirect methodActual mean method

Properties of simple correlation Symmetric Value lies between -1 and 1 Independent of change of origin and

scale Independent of unit of measurement Geometric mean of two regression

coefficient

Interpretation of correlation coefficient

Value of r

Interpretation

+1 Perfect positive correlation

-1 Perfect negative correlation

Close to +1

High degree of positive correlation

Close to -1

High degree of negative correlation

0 No correlation

Close to 0 Low degree of positive or negative correlation

Rank correlation method

Mathematical method for studying relationship between variables according to rank

Qualitative characteristics cannot be measured qualitatively but can be arranged in order

Merits of Rank correlation method

Easy to calculate Simple to understand Can be applied to any type of data

(Qualitative or Quantitative)

Demerits of Rank correlation method

Actual values are not used for calculations

Not convenient method for large samples

Role of Computer Technology in Statistics

SPSS is used by students later in their career

Can be used as an amplifierQuick computational abilities of massive figure

Can be used to produce many graphs quickly and easily